Space of modular forms of level 322, weight 2, and Character 322.g

• Label: 322.2.g
• Level: $322$
• Weight: $2$
• Character orbit: 322.g
• Rep. character: $\chi_{322}(45,\cdot)$
• Character field: $\Q(\zeta_{6})$
• Dimension: $32$
• Newform subspaces: $2$
• Sturm bound: $96$
• Trace bound: $2$

Defining parameters

Level:	\( N \)	\(=\)	\( 322 = 2 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	322.g (of order \(6\) and degree \(2\))
Character conductor:	\(\operatorname{cond}(\chi)\)	\(=\)	\( 161 \)
Character field:			\(\Q(\zeta_{6})\)
Newform subspaces:			\( 2 \)
Sturm bound:			\(96\)
Trace bound:			\(2\)
Distinguishing \(T_p\):			\(3\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(322, [\chi])\).

	Total	New	Old
Modular forms	104	32	72
Cusp forms	88	32	56
Eisenstein series	16	0	16

Trace form

\( 32 q - 16 q^{4} + 20 q^{9} + O(q^{10}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(322, [\chi])\) into newform subspaces

Label	Level	Weight	Char	Prim	Char order	Dim	Rel. Dim	$A$	Field	CM	Self-dual	Inner twists	Rank*	Traces				Coefficient ring index	Sato-Tate	$q$-expansion
														$a_{2}$	$a_{3}$	$a_{5}$	$a_{7}$
322.2.g.a	$322$	$2$	322.g	161.g	$6$	$16$	$8$	$2.571$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(-8\)	\(6\)	\(0\)	\(0\)	$7$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{5}q^{2}-\beta _{1}q^{3}+(-1+\beta _{5})q^{4}+\beta _{6}q^{5}+\cdots\)
322.2.g.b	$322$	$2$	322.g	161.g	$6$	$16$	$8$	$2.571$	\(\mathbb{Q}[x]/(x^{16} + \cdots)\)	None		$4$	$0$	\(8\)	\(-6\)	\(0\)	\(0\)	$1$	$\mathrm{SU}(2)[C_{6}]$	\(q-\beta _{6}q^{2}+\beta _{11}q^{3}+(-1-\beta _{6})q^{4}+\cdots\)

Decomposition of \(S_{2}^{\mathrm{old}}(322, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(322, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(161, [\chi])\)\(^{\oplus 2}\)